A154820 Numbers whose trajectory under iteration of sum of cubes of digits eventually turns out to follow the cyclic iteration of 133, 55, 250.

4, 13, 25, 28, 31, 40, 46, 52, 55, 64, 82, 103, 130, 133, 205, 208, 250, 256, 265, 280, 289, 298, 301, 310, 313, 331, 349, 394, 400, 406, 439, 448, 460, 484, 493, 502, 505, 520, 526, 550, 562, 589, 598, 604, 625, 640, 652, 679, 697, 769, 796, 802, 820, 829

Offset: 1

Author

Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 15 2009

Keywords

• nonn
• base

Comments

All the numbers are of the form 3n+1.

Subsequence of A165336. - Reinhard Zumkeller, Sep 17 2009

Examples

			Taking 40 for example,
  4^3 + 0^3 = 64;
  6^3 + 4^3 = 280;
  2^3 + 8^3 + 0^3 = 520;
  5^3 + 2^3 + 0^3 = 133;
  1^3 + 3^3 + 3^3 = 55;
  5^3 + 5^3 = 250.
		

Crossrefs

Cf. A165337, A154877, A165336, A165339.

Programs

Maple

A055012 := proc(n) local a,d ; a := 0 ; for d in convert(n,base,10) do a := a+d^3; od; a ; end: isA154820 := proc(n) local traj,t ; t := n ; traj := {} ; while true do if t in traj then if t in {133,55,250} then RETURN(true) ; else RETURN(false) ; fi; else traj := traj union {t} ; t := A055012(t) ; fi; od: end: for n from 1 to 1000 do if isA154820(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Jan 18 2009

Extensions

Extended by R. J. Mathar, Jan 18 2009

Edited by Charles R Greathouse IV, Aug 02 2010